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Math Help - Integration Problem

  1. #1
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    Integration Problem

    Hello, I'm new here and I have a problem that I can't solve. I thank you in advance for ANY help you can give me. I know things are written to scale, but I couldn't find where to access the symbols. Thank you so much!



    ∫ x - 1
    ----------dx
    2
    x - 4x + 5

    this bottom x is squared and the -- lines are the divided by lines. Then the formula is multiplied by dx. Thanks!

    Cindi
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Cindi24 View Post
    Hello, I'm new here and I have a problem that I can't solve. I thank you in advance for ANY help you can give me. I know things are written to scale, but I couldn't find where to access the symbols. Thank you so much!



    ∫ x - 1
    ----------dx
    2
    x - 4x + 5

    this bottom x is squared and the -- lines are the divided by lines. Then the formula is multiplied by dx. Thanks!

    Cindi
    note that \int \frac {x - 1}{x^2 - 4x + 5}~dx = \frac 12 \int \frac {2x - 2}{x^2 - 4x + 5}~dx  = \frac 12 \int \frac {2x - 4 + 2}{x^2 - 4x + 5}~dx = \frac 12 \int \frac {2x - 4}{x^2 - 4x + 5}~dx + \int \frac 1{x^2 - 4x + 5}~dx

    for the first integral, do a substitution of u = x^2 - 4x + 5, for the second, complete the square in the denominator, and try to get the arctangent integral.

    can you continue?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by o_O View Post
    \frac{x-1}{x^{2}-4x+5} = \frac{x-1}{(x+5)(x-1)} = \frac{1}{x+5}

    Easier to deal with?
    that's not true. if you expand the denominator of what you wrote, you get x^2 + 4x - 5
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  4. #4
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    oh, okay! I think so. Thank you!
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  5. #5
    o_O
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    Ah whoops my bad. Don't know what I was thinking =S
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by o_O View Post
    Ah whoops my bad. Don't know what I was thinking =S
    hehe, i thought the same thing at first, but then i realized the factorization doesn't work, so i had to do it the hard way
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